Chapter 4.2, Problem 14OE

To determine

To State: The degree of the polynomial $p^2{q}^3-3p{q}^4$ and to say if it is a binomial or a trinomial.

Answer to Problem 14OE

The required degree of the binomial $p^2{q}^3-3p{q}^4$ is 5.

Explanation of Solution

Given information:

The polynomial $p^2{q}^3-3p{q}^4$

Calculation:

The degree of a polynomial is the greatest of the degree of its terms after it has been simplified

  $p^2{q}^3-3p{q}^4$

The degree of the term $p^2{q}^3$ is $2+3=5$ .

The degree of the term $-3p^4$ is $1+4=5$ .

The greatest degree is 5.

So, the degree of the polynomial $p^2{q}^3-3p{q}^4$ is 5.

Since the polynomial has two terms, it is a binomial.